Figure 2-3: (a) Rheostat is used to set the resistance between terminals 1 and 2 at any value between zero and Rmax; (b) location of wiper in
|
|
- Rose McDowell
- 7 years ago
- Views:
Transcription
1
2
3 Figure 2-3: (a) Rheostat is used to set the resistance between terminals 1 and 2 at any value between zero and Rmax; (b) location of wiper in potentiometer divides the resistance Rmax among R13 and R23.
4 Circuit Elements: Independent Sources
5 Circuit Elements: Dependent Sources
6 Kirchoff s laws: A node is a point where two are more circuit elements meet. Kirchoff s Current Law (KCL): The algebraic sum of all the currents at any node in a circuit equals zero. A closed-path or loop: Starting at any arbitrary node, walk along an element connected to it to move to another node, repeat this as often as necessary, and come back to the original node. The path you traced is a closed path or loop. Kirchoff s Voltage Law (KVL): The algebraic sum of all the voltages around any closed-path in a circuit equals zero.
7
8 Two important types of interconnection of circuit components: Series Connection: Two or more elements (branches, components) are said to be interconnected in series if the currents through each one of them are equal. Parallel Connection: Two or more elements (branches, components) are said to be interconnected in parallel if the voltages across each one of them are equal. In the following diagrams, two elements are interconnected forming an equivalent one element with two terminals a and b. Decide as far as the terminals a and b are concerned, whether the two elements are interconnected in series or in parallel.
9
10
11 Principles of Electrical Engineering I Interconnection of Sources v 1 v 2 i v v 1 v 2 i v Voltage sources connected in series Voltage sources connected in parallel i 1 i 2 i v i i 1 i 2 v Current sources connected in series Current sources connected in parallel All interconnections that do not satisfy Kirchoff s laws are illegal. Illustration of illegal interconnections: 3A 12V 9V 4A 3Ω
12 We often use two phrases `open circuit' between two terminals or `short circuit' between two terminals. In the following figure, terminals 1 and 2 are open circuited, while terminals 3 and 4 are short circuited. The terminology applies to only those specified terminals. A voltmeter reads the voltage across an element, as such it is connected across (or parallel) to the element. An ammeter reads the current through an element, as such it is connected in series to the element.
13 Basics you should always remember Electric Potential by itself is not power. Current has to be supplied or consumed to generate power. In other words, the interaction of Electric Potential and Electric current causes power to be generated or consumed. In the same way, your inherent potential by itself is not enough, it needs to be put to work by doing Home-Work in order to learn the material properly. Then only circuit analysis in its full detail can be absorbed by you. Voltage is across a branch and current is through a branch: i v Power generated by the small box = vi i v Power absorbed by the small box = vi Figure 1 Resistance: Water flows down the hill unless it is being pumped up. Current flows down the potential hill through a resistance. Resistance is a passive element. It always consumes power. Figure 2 Source is an active element. A source could pump the current up the potential hill and thus generate power. A source could have a current flowing down the potential hill and thus consume power; in this case it is a sink. Think of a good battery charging a weak one. In the figure given on the right, two batteries a good one (denoted by α) and a weak one (denoted by β) are interconnected at terminals a and b. Which of the two batteries generates power and which one consumes? Is i positive if v is positive? i R i i v = Ri R v = Ri R v = Ri I Z V = ZI, Z is the impedance α i b - v a β v i β For a voltage source, v is prescribed, and i depends on the circuit β. v i β For a current source, i is prescribed, and v depends on the circuit β. Voltage Source Current Source
14 In circuit analysis, different situations arise. Both the voltage and the current of a branch might be known ahead. In this case the branch info is completely known. Either voltage or current of a branch but not both are known. Neither voltage nor current of a branch are known. In the case of a voltage source, voltage is known ahead but not current. That is, the voltage of a voltage source is prescribed ahead but the current through it is a variable that depends on the network to which it is connected. In the case of a current source, current is known ahead but not voltage. That is, the current of a current source is prescribed ahead but the voltage across it is a variable that depends on the network to which it is connected. 2A i = 6A 12V 2Ω i = 2A 2Ω 4V i = 4A 12V 3Ω 2A i = 2A 4Ω 8V i = 0 12V Open Circuit 2A i = 2A In the case of a resistance, the ratio between voltage and current (via Ohms s law) is known. If a voltage or current is unknown, you can assign a variable to it. If we do so for each branch in the circuit, we end up with some unknown variables. The aim of circuit analysis is to write as many equations (via KCL, KVL, Ohms s law) as there are unknown variables, and then solve those equations to determine the unknown variables. The entire circuit analysis involves only this type of work. All we do in this course is to develop ways of simplifying the method(s) of writing equations, as small in number as needed. 0 V - Short Circuit Nodal Analysis: Consider a resistance R with two terminals marked A and B. Suppose the voltage of terminals A and B with respect to the ground G are respectively v a and v b as shown. Then the voltage across R is v = v a v b, and the current through R is i = vav b R. v a A i R v v b B G Mesh Analysis: Consider a resistance R having two currents i 1 and i 2 pumped into it as shown. Then the net current through it is i = i 1 i 2, and the voltage across R is v = R(i 1 i 2 ). i i 1 v R i 2 We will deal extensively with both Nodal Analysis and Mesh Analysis later on. 2
15 Principles of Electrical Engineering I Modeling of Practical Sources All physical devices need to be modeled appropriately in terms of circuit elements so that their characteristics can be taken into account in circuit analysis. In this notes, we emphasize modeling of practical voltage and current sources. Modeling of a practical voltage source: An ideal voltage source keeps the voltage across its terminals the same whatever might be the current (and thus the power) it supplies to a load. Obviously, a practical voltage source can never do so because of its own internal behavior. The voltage across the terminals of a practical voltage source drops more and more as it supplies more and more current. As such, a practical voltage source can be modeled as an ideal voltage source in series with a resistance that can appropriately be called as its internal resistance (in general, impedance). Figure 1 shows a practical voltage source (denoted by α) whose terminals are a and b. A load β when connected to the source draws a current from it. A circuit model of a practical voltage source is shown in Figure 2 along with the load β. Practical Source α i b - v β Load a Figure 1 Model of a Practical Voltage Source i b R g v g v β Load - a Figure 2 i (A) v (V) Table 1 In what follows, we illustrate by an example how to compute v g and R g for a given set of data, and also compute the range of current over which the circuit model of the given practical voltage source is valid. Example 1: A set of experimental data is shown in Table 1 for a practical voltage source. The measurements are obtained experimentally showing how the voltage v across the terminals of a given practical voltage source changes as the current i it supplies to the load varies. Consider the model shown in Figure 2, and determine v g and R g, and the region in which the model is valid.
16 2 Modeling of a practical current source: An ideal current source keeps the current it supplies to a load the same whatever might be the voltage (and thus the power) a load demands. Obviously, a practical current source can never do so because of certain leakages inherent internal to it. The current it supplies to the load decreases as the voltage the load demands increases. As such, a practical current source can be modeled as an ideal current source in parallel with a resistance that can appropriately be called as its internal resistance or leakage resistance. Figure 1 shows a practical current source (denoted by α) whose terminals are a and b. A load β when connected to the source demands a voltage across it. A circuit model of a practical current source is shown in Figure 3 along with the load β. Practical Source α i b - v β Load a Figure 1 i g Model of a Practical Current Source R g Figure 3 i b v β Load - a v (V) i (ma) Table 2 In what follows, we illustrate by an example how to compute i g and R g for a given set of data, and also compute the range of voltage over which the circuit model of the given practical current source is valid. Example 2: A set of experimental data is shown in Table 2 for a practical current source. The measurements are obtained experimentally showing how the current i through the terminals of a given practical current source changes as the voltage v it supplies to the load varies. Consider the model shown in Figure 3, and determine i g and R g, and the region in which the model is valid.
17 Principles of Electrical Engineering I A Transistor Amplifier Circuit v in G R B C Q B E Transistor R C v o v g G i b R B B r p v be E g m v be C Transistor Equivalent r o R C v o The circuit on the left is a simple amplifier circuit containing a device called a transistor (the circled component, denoted by Q) having three terminals B, E, and C. Note: The transistor circuit given here is missing its bias voltages which make it work. You will learn the specifics of this circuit in a later course. For some bias voltages, the so called small signal equivalent circuit of transistor circuit is shown on the right. Here r p is the resistance of the so called plate between B and E, g m is the transconductance of the transistor, and r o is the output resistance associated with the transistor. The ratio of the output voltage v o to the input voltage v in is called the amplifier gain A. Compute A. See the other side for a design example.
18 2 A design example: A pressure-gauge generates a voltage proportional to the pressure exerted on it. However, the magnitude of voltage generated is small and need a very sensitive meter to read it. As such, for proper reading, one needs to amplify the voltage generated by the pressure-gauge. The transistor amplifier circuit shown on the other side is to be used to amplify the voltage close to 200 fold, i.e., the amplifier gain A needs to be as close as possible to 200. For the circuit shown (on the other side) v in is the voltage generated by the pressure-gauge. A design engineer, based on other considerations, decides to use R B = 400Ω and R C = 8KΩ, and then looks for an appropriate transistor. He/she finds in a catalog three different transistors whose parameters are tabulated below. Which of the three transistors is the most appropriate one to be used? Transistor r p in KΩ g m r o in KΩ Hint: Determine the gain A for each transistor
19
20 332:221 Principles of Electrical Engineering I Tracing a Circuit Determine v x in the circuit shown. a 5A b 50Ω vx c 20Ω d 200Ω e 0.275v x f Often the practical layout of a circuit is completely different to the one required for easy analysis. It is hard to see what is going on in the circuit given above unless you are well experienced. The circuit given needs to be retraced so that all the interconnections are clear. How do we retrace a circuit? Hint: The circuit branches or components between any two nodes in the given circuit as well as the re-traced circuit must be the same, otherwise the given circuit and the re-traced circuit are not equivalent. The retraced circuit is as shown on the right (justify it). We can now write the following equation easily, [ v x ] 5 = a, c, e b, d, f 5A 50Ω vx 20Ω 200Ω 0.275v x This yields v x = 25 V. Having determined v x, we can find next the current in each resistance easily.
21 Principles of Electrical Engineering I Example 1: KCL-KVL Examples Consider the partially solved circuit on the right with α = 10.5 and β = 5. 3 Determine i 1, i x, αi x, i 2, v d, and v g in the order given. Hints: B To determine i x, write a KVL equation around BGCB. To determine i 1, write a KCL equation at C. αi x is easy to determine once i x is known. To determine i 2, write a KCL equation at A. To determine v d, write a KVL equation around AGBA. To determine v g, write a KVL equation around DGCD. αi x =? 10Ω 16A G 60V A 5Ω i 2 =? 12Ω B - v d =? βi 1 D 9 A 5A 10A Ω i x =? v g =? i 1 =? C The complete solution which satisfies both the branch constraints and the intersection constraints is as shown on the right (justify it). 9A αi x = 21A Ω 10Ω 170V i 1 = 12A A 16A G 60V 5Ω i x = 2A C i 2 = 5A 40V βi 1 12Ω - 5A 10A D
22 2 Cutset: Kirchoff s Current Law(KCL) is normally written at a node where several branches meet. KCL can also be written for what are known as cutsets. A cutset of a circuit is a set of branches which when cut divides the circuit into two parts. Let one side of a cutset be denoted as side N and the other side as Side S. Then, KCL states that the sum of currents going from side N to side S equals the sum of currents going from side S to side N. B Example 2: In the circuit shown ontheright, determine i 2 and i 5 by using node equations or cutset equations. 5A R4 N S 16A G 60V A C R 3 i 2 =? i 5 =? N S 10A R 2 R 5 R 1 D v in G i b R B B r p v be E C i x g m v be R C v o Example 3: Determine i x in the circuit shown on the left. The answer is zero. Justify it. Example 4: Some times one does not need to solve the entire circuit to determine just what is needed. In the circuit on the right, determine the output voltage v o. 1Ω i ba B R 1 C 3iy R 2 6A A 3A v o 3Ω i o R 3 G 1Ω 4i x i x D 5A F R 4 i y E
23
24 Principles of Electrical Engineering I Determination of open circuit voltage v oc : We note that there is no current through 10Ω resistance. Hence v x = 0. Thus is v oc is same as v oc. This implies that the dependent source current is zero. It is also easy to see that the 2 A current source simply supplies the 5Ω resistance establishing 10 V across it. The open circuit voltage at the terminals a and b is the same as the voltage across the 5Ω resistance, that is 10 V. Thus v oc = 10 V. 10Ω vx b 10Ω vx b 2A 5Ω 0.7v x 2A 5Ω 0.7v x a a 2A 5Ω 10Ω vx 0.7v x b a Determination of Short Circuit Current i sh : Consider the circuit shown where the terminals a and b are short circuited. Mark the unknown node voltage as v 1 with respect to the ground. Note that v x = v 1. We can then write the relevant KCL equation as 2A 5Ω v 1 v x b 10Ω 0.7v x a i sh v 1 10 v 1 5 = 0.7v x 2 = 0.7v 1 2. By solving the above equation, we get v 1 = 5 V. Thus i sh = v 1 = 0.5 A. 10
25 332:221 Principles of Electrical Engineering I Home-work: try to do the problem yourself before reading the solution given on the next page. Consider the circuit shown. We are interested in determining i a, i b, and i c. Use Kirchoff s current law systematically and repetitively to determine them. Q 2A R 1A 3A L i 1 i 2 M N P 5A G i 3 H J K i4 4A 3i 2 2i 1 C D E F i a 3i 4 2i 3 2i 2 i b A i c B
26 2 Solution: Write the KCL equations at the following nodes in that order to solve for each branch current: Node Q, Node R, Node L, Node M, Node P, Node N, Node G, Node H, Node K, Node J, Node C, Node F, Node E Node B, Node A, and Node D. One of the above equations just acts as a check or verification. The answers are i 1 = 1 A, i 2 = 1 A, i 3 = 3 A, i 4 = 2 A, i a = 2 A, i b = 2 A, and i c = 4 A. In this problem, we just tried to illustrate Kirchoff s current law. We could solve here for the required currents by using only Kirchoff s current law. In a general circuit analysis we need both Kirchoff s current and voltage laws to determine the required variables. We will learn how to use these laws as we progress with the course.
27 332:221 Principles of Electrical Engineering I Home-work: try to do the problem yourself before reading the solution given on the next page. Consider the circuit shown. We are interested in determining v c, v d, v e, v f, v j, and v k. Use Kirchoff s voltage law systematically and repetitively to determine them. 10V 20V 30V 3v 4 A M v 1 v 3 B L v 2 v 4 C K v c v k D J v d v j 2v 4 v e E F H 3v 3 v f 2 2v 2v 1 40V 50V 60V G1 G2 G3 G4 G5 G7 G8 G9 G10 G11 G6
28 2 Solution: Write the KVL equations for the following loops in that order to solve for each branch voltage: loop G1ABG2G1, loop G2BCG3G2, loop G11MLG10G11, loop G10LKG9G10, loop G3CDG4G3, loop G4DEG5G4, loop G9KJG8G9, loop G8JHG7G8, loop G7HFG6G7, and loop G5EFG6G5. The answers are v 1 = 30 V, v 2 = 50 V, v 3 = 110 V, v 4 = 90 V, v c = 240 V, v d = 60 V, v e = 610 V, v f = 280 V, v j = 40 V, and v k = 100 V. In this problem, we just tried to illustrate Kirchoff s voltage law. We could solve here for the required voltages by using only Kirchoff s voltage law. In a general circuit analysis we need both Kirchoff s current and voltage laws to determine the required variables. We will learn how to use these laws as we progress with the course.
29 Tracing Circuits Example-1 Show or argue that the following four circuits are equivalent. Do it yourself first before reading the solution given below. L M N A G E Z 4 v g i g ki x Z 3 B Z 1 C i x Z 2 D B Z 1 C i x Z 2 D ki x Z 3 Z 4 v g i g A G E L M N N M L E G A i g v g Z 4 Z 3 ki x D Z 2 C i x Z 1 B D Z 2 C i x Z 1 B Z 3 ki x i g v g Z 4 E G A N M L Note: Note that how the circuit is drawn is not important although visually one could feel better with one way of drawing the circuit than the other. What is important is what is connected between any two designated nodes. Solution: Although the physical configuration or layout of each circuit is different, all the above circuits have exactly the same nodes, and moreover in between any two given nodes exactly the same branches exist. As such, all the circuits are electrically equivalent.
30 332:221 Principles of Electrical Engineering I FALL 2005 Quiz 1 This design problem is a home-work which will be collected and graded. Consider the circuit shown. By writing a KCL at an appropriate node, determine i s. v α b c d α i s v 5i β β s 20V 7A a 2A f Figure 1 e Determine the voltage across the dependent source in the direction shown. By writing a KVL around an appropriate loop, determine the voltage v α across the element α in the direction shown. By writing a KVL around an appropriate loop, determine the voltage v β across the element β in the direction shown. Fill the following table regarding power consumption or generation. A particular element either consumes or generates power. You must put the appropriate value for a particular element in only one of the unfilled columns whichever is appropriate. Element Power Consumed Power Generated Element α Element β Independent Source Dependent Source
31 Consider the so called bridged T circuit that occurs commonly in applications. Some one partially solved the circuit shown on the right and determined v Ge as 12 V. Determine the following by using appropriately, Ohm s law, KVL, and KCL. At each step, state the law you used. Bridged Tee Example c 24V k a i a 2i x d v Ge G 3.6Ω vba e i e 6Ω vfe Determine the voltage of the controlled source 2i x and then determine the controlling current i x. You may write the KVL for the loop kcdegk. 4Ω f b v mh m h i x 1Ω After knowing i x, determine v mh. Determine v fe by using an appropriate KVL (look for a closed path which by now has only v fe as unknown). Determine i e (Use Ohm s law, note that v fe is known by now). Determine i a by using the KCL at the node h. Proceeding in the same way solve for the current in each branch (mark the current values on the circuit) and verify whatever you have done above is correct. That is KCL equation at each node is satisfied and all three meshes, kcdegk, efhmge, and abfeda, satisfy KVL equations.
32 Principles of Electrical Engineering I This Home-Work problem is collected and graded Determination of voltage of node b with respect to node a: This can be done by a number of ways. At this time, we can use KCL and KVL judiciously in a straight forward way. Step 1: Write a KCL at node e to determine the current in 10Ω resistance in terms of the variable i x (Note that i x is yet unknown). 26V i x 2Ω 3Ω 10Ω 0.5i x b G a Step 2: Write a KVL around the closed-loop GcdefG. Solve it to determine i x. Step 3: Walk along the path afgcdb and algebraically add the voltages encountered to determine the voltage of node b with respect to node a.
33 Principles of Electrical Engineering I Determination of short circuit current i sh : This can be done by a number of ways. At this time, we can use KCL and KVL judiciously in a straight forward way. Step 1: Write a KVL for the closed-loop afgcdba to determine i x. 26V i x 2Ω 3Ω b i sh 10Ω 0.5i x G a Step 2: Write a KCL at node d to determine the current in 3Ω resistance in terms of i x and i sh (Note that the variable i sh is yet unknown). Step 3: Write a KCL at node e to determine the current in 10Ω resistance in terms of i x and i sh (Note that the variable i sh is yet unknown). Step 4: Write a KVL for the closed-loop afedba and determine i sh.
Nodal and Loop Analysis
Nodal and Loop Analysis The process of analyzing circuits can sometimes be a difficult task to do. Examining a circuit with the node or loop methods can reduce the amount of time required to get important
More informationMesh-Current Method (Loop Analysis)
Mesh-Current Method (Loop Analysis) Nodal analysis was developed by applying KCL at each non-reference node. Mesh-Current method is developed by applying KVL around meshes in the circuit. A mesh is a loop
More informationDC mesh current analysis
DC mesh current analysis This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,
More informationCircuits 1 M H Miller
Introduction to Graph Theory Introduction These notes are primarily a digression to provide general background remarks. The subject is an efficient procedure for the determination of voltages and currents
More informationLecture Notes: ECS 203 Basic Electrical Engineering Semester 1/2010. Dr.Prapun Suksompong 1 June 16, 2010
Sirindhorn International Institute of Technology Thammasat University School of Information, Computer and Communication Technology Lecture Notes: ECS 203 Basic Electrical Engineering Semester 1/2010 Dr.Prapun
More informationSeries and Parallel Circuits
Direct Current (DC) Direct current (DC) is the unidirectional flow of electric charge. The term DC is used to refer to power systems that use refer to the constant (not changing with time), mean (average)
More informationCircuit Analysis using the Node and Mesh Methods
Circuit Analysis using the Node and Mesh Methods We have seen that using Kirchhoff s laws and Ohm s law we can analyze any circuit to determine the operating conditions (the currents and voltages). The
More informationExperiment #5, Series and Parallel Circuits, Kirchhoff s Laws
Physics 182 Summer 2013 Experiment #5 1 Experiment #5, Series and Parallel Circuits, Kirchhoff s Laws 1 Purpose Our purpose is to explore and validate Kirchhoff s laws as a way to better understanding
More informationV out. Figure 1: A voltage divider on the left, and potentiometer on the right.
Living with the Lab Fall 202 Voltage Dividers and Potentiometers Gerald Recktenwald v: November 26, 202 gerry@me.pdx.edu Introduction Voltage dividers and potentiometers are passive circuit components
More informationBasic Electronics Prof. Dr. Chitralekha Mahanta Department of Electronics and Communication Engineering Indian Institute of Technology, Guwahati
Basic Electronics Prof. Dr. Chitralekha Mahanta Department of Electronics and Communication Engineering Indian Institute of Technology, Guwahati Module: 2 Bipolar Junction Transistors Lecture-2 Transistor
More informationW03 Analysis of DC Circuits. Yrd. Doç. Dr. Aytaç Gören
W03 Analysis of DC Circuits Yrd. Doç. Dr. Aytaç Gören ELK 2018 - Contents W01 Basic Concepts in Electronics W02 AC to DC Conversion W03 Analysis of DC Circuits (self and condenser) W04 Transistors and
More informationSeries and Parallel Resistive Circuits
Series and Parallel Resistive Circuits The configuration of circuit elements clearly affects the behaviour of a circuit. Resistors connected in series or in parallel are very common in a circuit and act
More information120 CHAPTER 3 NODAL AND LOOP ANALYSIS TECHNIQUES SUMMARY PROBLEMS SECTION 3.1
IRWI03_082132v3 8/26/04 9:41 AM Page 120 120 CHAPTER 3 NODAL AND LOOP ANALYSIS TECHNIQUES SUMMARY Nodal analysis for an Nnode circuit Select one node in the Nnode circuit as the reference node. Assume
More informationPHYSICS 111 LABORATORY Experiment #3 Current, Voltage and Resistance in Series and Parallel Circuits
PHYSCS 111 LABORATORY Experiment #3 Current, Voltage and Resistance in Series and Parallel Circuits This experiment is designed to investigate the relationship between current and potential in simple series
More informationChapter 1. Fundamental Electrical Concepts
Chapter 1 Fundamental Electrical Concepts Charge, current, voltage, power circuits, nodes, branches Branch and node voltages, Kirchhoff Laws Basic circuit elements, combinations 01 fundamental 1 1.3 Electrical
More informationModule 2. DC Circuit. Version 2 EE IIT, Kharagpur
Module DC Circuit Lesson 4 Loop Analysis of resistive circuit in the context of dc voltages and currents Objectives Meaning of circuit analysis; distinguish between the terms mesh and loop. To provide
More information1. Introduction and Chapter Objectives
Real Analog Circuits 1 Chapter 1: Circuit Analysis Fundamentals 1. Introduction and Chapter Objectives In this chapter, we introduce all fundamental concepts associated with circuit analysis. Electrical
More informationExperiment NO.3 Series and parallel connection
Experiment NO.3 Series and parallel connection Object To study the properties of series and parallel connection. Apparatus 1. DC circuit training system 2. Set of wires. 3. DC Power supply 4. Digital A.V.O.
More informationLAB2 Resistors, Simple Resistive Circuits in Series and Parallel Objective:
LAB2 Resistors, Simple Resistive Circuits in Series and Parallel Objective: In this lab, you will become familiar with resistors and potentiometers and will learn how to measure resistance. You will also
More informationExample: Determine the power supplied by each of the sources, independent and dependent, in this circuit:
Example: Determine the power supplied by each of the sources, independent and dependent, in this circuit: Solution: We ll begin by choosing the bottom node to be the reference node. Next we ll label the
More informationAnalysis of a single-loop circuit using the KVL method
Analysis of a single-loop circuit using the KVL method Figure 1 is our circuit to analyze. We shall attempt to determine the current through each element, the voltage across each element, and the power
More informationHow To Find The Current Of A Circuit
The node voltage method Equivalent resistance Voltage / current dividers Source transformations Node voltages Mesh currents Superposition Not every circuit lends itself to short-cut methods. Sometimes
More informationBasic Laws Circuit Theorems Methods of Network Analysis Non-Linear Devices and Simulation Models
EE Modul 1: Electric Circuits Theory Basic Laws Circuit Theorems Methods of Network Analysis Non-Linear Devices and Simulation Models EE Modul 1: Electric Circuits Theory Current, Voltage, Impedance Ohm
More informationCurrent and Voltage Measurements. Current measurement
Current and oltage easurements Current measurement ccording to current continuity (i.e. charge conservation) law, the current can be measured in any portion of a single loop circuit. B Circuit Element
More informationChapter 5. Parallel Circuits ISU EE. C.Y. Lee
Chapter 5 Parallel Circuits Objectives Identify a parallel circuit Determine the voltage across each parallel branch Apply Kirchhoff s current law Determine total parallel resistance Apply Ohm s law in
More informationTransistor Characteristics and Single Transistor Amplifier Sept. 8, 1997
Physics 623 Transistor Characteristics and Single Transistor Amplifier Sept. 8, 1997 1 Purpose To measure and understand the common emitter transistor characteristic curves. To use the base current gain
More informationBJT AC Analysis. by Kenneth A. Kuhn Oct. 20, 2001, rev Aug. 31, 2008
by Kenneth A. Kuhn Oct. 20, 2001, rev Aug. 31, 2008 Introduction This note will discuss AC analysis using the beta, re transistor model shown in Figure 1 for the three types of amplifiers: common-emitter,
More informationOPERATIONAL AMPLIFIERS
INTRODUCTION OPERATIONAL AMPLIFIERS The student will be introduced to the application and analysis of operational amplifiers in this laboratory experiment. The student will apply circuit analysis techniques
More informationSchool of Engineering Department of Electrical and Computer Engineering
1 School of Engineering Department of Electrical and Computer Engineering 332:223 Principles of Electrical Engineering I Laboratory Experiment #4 Title: Operational Amplifiers 1 Introduction Objectives
More informationAfter completing this chapter, the student should be able to:
DC Circuits OBJECTIVES After completing this chapter, the student should be able to: Solve for all unknown values (current, voltage, resistance, and power) in a series, parallel, or series-parallel circuit.
More informationLesson Plan. Parallel Resistive Circuits Part 1 Electronics
Parallel Resistive Circuits Part 1 Electronics Lesson Plan Performance Objective At the end of the lesson, students will demonstrate the ability to apply problem solving and analytical techniques to calculate
More information2.1 Introduction. 2.2 Terms and definitions
.1 Introduction An important step in the procedure for solving any circuit problem consists first in selecting a number of independent branch currents as (known as loop currents or mesh currents) variables,
More informationPeople s Physics Book
The Big Ideas: The name electric current is given to the phenomenon that occurs when an electric field moves down a wire at close to the speed of light. Voltage is the electrical energy density (energy
More informationSeries and Parallel Circuits
Series and Parallel Circuits Components in a circuit can be connected in series or parallel. A series arrangement of components is where they are inline with each other, i.e. connected end-to-end. A parallel
More informationThevenin Equivalent Circuits
hevenin Equivalent Circuits Introduction In each of these problems, we are shown a circuit and its hevenin or Norton equivalent circuit. he hevenin and Norton equivalent circuits are described using three
More informationCHAPTER 28 ELECTRIC CIRCUITS
CHAPTER 8 ELECTRIC CIRCUITS 1. Sketch a circuit diagram for a circuit that includes a resistor R 1 connected to the positive terminal of a battery, a pair of parallel resistors R and R connected to the
More informationParallel DC circuits
Parallel DC circuits This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,
More informationScaling and Biasing Analog Signals
Scaling and Biasing Analog Signals November 2007 Introduction Scaling and biasing the range and offset of analog signals is a useful skill for working with a variety of electronics. Not only can it interface
More informationKirchhoff's Current Law (KCL)
Kirchhoff's Current Law (KCL) I. Charge (current flow) conservation law (the Kirchhoff s Current law) Pipe Pipe Pipe 3 Total volume of water per second flowing through pipe = total volume of water per
More informationChapter 7 Direct-Current Circuits
Chapter 7 Direct-Current Circuits 7. Introduction...7-7. Electromotive Force...7-3 7.3 Resistors in Series and in Parallel...7-5 7.4 Kirchhoff s Circuit Rules...7-7 7.5 Voltage-Current Measurements...7-9
More information= (0.400 A) (4.80 V) = 1.92 W = (0.400 A) (7.20 V) = 2.88 W
Physics 2220 Module 06 Homework 0. What are the magnitude and direction of the current in the 8 Ω resister in the figure? Assume the current is moving clockwise. Then use Kirchhoff's second rule: 3.00
More informationElectrical Fundamentals Module 3: Parallel Circuits
Electrical Fundamentals Module 3: Parallel Circuits PREPARED BY IAT Curriculum Unit August 2008 Institute of Applied Technology, 2008 ATE310- Electrical Fundamentals 2 Module 3 Parallel Circuits Module
More informationBasic Principles of. Electricity. Basic Principles of Electricity. by Prof. Dr. Osman SEVAİOĞLU Electrical and Electronics Engineering Department
Basic Principles of Electricity METU by Prof. Dr. Osman SEVAİOĞLU Electrical and Electronics Engineering Department EE 209 Fundamentals of Electrical and Electronics Engineering, Prof. Dr. O. SEVAİOĞLU,
More informationCircuits. The light bulbs in the circuits below are identical. Which configuration produces more light? (a) circuit I (b) circuit II (c) both the same
Circuits The light bulbs in the circuits below are identical. Which configuration produces more light? (a) circuit I (b) circuit II (c) both the same Circuit II has ½ current of each branch of circuit
More informationPreamble. Kirchoff Voltage Law (KVL) Series Resistors. In this section of my lectures we will be. resistor arrangements; series and
Preamble Series and Parallel Circuits Physics, 8th Edition Custom Edition Cutnell & Johnson Chapter 0.6-0.8, 0.0 Pages 60-68, 69-6 n this section of my lectures we will be developing the two common types
More informationTECHNIQUES OF. C.T. Pan 1. C.T. Pan
TECHNIQUES OF CIRCUIT ANALYSIS C.T. Pan 1 4.1 Introduction 4.2 The Node-Voltage Method ( Nodal Analysis ) 4.3 The Mesh-Current Method ( Mesh Analysis ) 4.4 Fundamental Loop Analysis 4.5 Fundamental Cutset
More informationSTUDY MATERIAL FOR CLASS 10+2 - Physics- CURRENT ELECTRICITY. The flow of electric charges in a particular direction constitutes electric current.
Chapter : 3 Current Electricity Current Electricity The branch of Physics which deals with the study of electric charges in motion is called current electricity. Electric current The flow of electric charges
More informationFirst Year (Electrical & Electronics Engineering)
Z PRACTICAL WORK BOOK For The Course EE-113 Basic Electrical Engineering For First Year (Electrical & Electronics Engineering) Name of Student: Class: Batch : Discipline: Class Roll No.: Examination Seat
More informationSeries-Parallel Circuits. Objectives
Series-Parallel Circuits Objectives Identify series-parallel configuration Analyze series-parallel circuits Apply KVL and KCL to the series-parallel circuits Analyze loaded voltage dividers Determine the
More informationPhysics 623 Transistor Characteristics and Single Transistor Amplifier Sept. 13, 2006
Physics 623 Transistor Characteristics and Single Transistor Amplifier Sept. 13, 2006 1 Purpose To measure and understand the common emitter transistor characteristic curves. To use the base current gain
More informationFig. 1 Analogue Multimeter Fig.2 Digital Multimeter
ELECTRICAL INSTRUMENT AND MEASUREMENT Electrical measuring instruments are devices used to measure electrical quantities such as electric current, voltage, resistance, electrical power and energy. MULTIMETERS
More informationVer 3537 E1.1 Analysis of Circuits (2014) E1.1 Circuit Analysis. Problem Sheet 1 (Lectures 1 & 2)
Ver 3537 E. Analysis of Circuits () Key: [A]= easy... [E]=hard E. Circuit Analysis Problem Sheet (Lectures & ). [A] One of the following circuits is a series circuit and the other is a parallel circuit.
More informationSERIES-PARALLEL DC CIRCUITS
Name: Date: Course and Section: Instructor: EXPERIMENT 1 SERIES-PARALLEL DC CIRCUITS OBJECTIVES 1. Test the theoretical analysis of series-parallel networks through direct measurements. 2. Improve skills
More informationLight Bulbs in Parallel Circuits
Light Bulbs in Parallel Circuits In the last activity, we analyzed several different series circuits. In a series circuit, there is only one complete pathway for the charge to travel. Here are the basic
More informationVoltage Divider Bias
Voltage Divider Bias ENGI 242 ELEC 222 BJT Biasing 3 For the Voltage Divider Bias Configurations Draw Equivalent Input circuit Draw Equivalent Output circuit Write necessary KVL and KCL Equations Determine
More informationParallel and Series Resistors, Kirchoff s Law
Experiment 2 31 Kuwait University Physics 107 Physics Department Parallel and Series Resistors, Kirchoff s Law Introduction In this experiment the relations among voltages, currents and resistances for
More informationLab 3 - DC Circuits and Ohm s Law
Lab 3 DC Circuits and Ohm s Law L3-1 Name Date Partners Lab 3 - DC Circuits and Ohm s Law OBJECTIES To learn to apply the concept of potential difference (voltage) to explain the action of a battery in
More informationSeries and Parallel Circuits
Series and Parallel Circuits Direct-Current Series Circuits A series circuit is a circuit in which the components are connected in a line, one after the other, like railroad cars on a single track. There
More informationSecond Order Linear Nonhomogeneous Differential Equations; Method of Undetermined Coefficients. y + p(t) y + q(t) y = g(t), g(t) 0.
Second Order Linear Nonhomogeneous Differential Equations; Method of Undetermined Coefficients We will now turn our attention to nonhomogeneous second order linear equations, equations with the standard
More informationAP Physics Electricity and Magnetism #4 Electrical Circuits, Kirchoff s Rules
Name Period AP Physics Electricity and Magnetism #4 Electrical Circuits, Kirchoff s Rules Dr. Campbell 1. Four 240 Ω light bulbs are connected in series. What is the total resistance of the circuit? What
More informationKirchhoff s Laws Physics Lab IX
Kirchhoff s Laws Physics Lab IX Objective In the set of experiments, the theoretical relationships between the voltages and the currents in circuits containing several batteries and resistors in a network,
More informationBJT Amplifier Circuits
JT Amplifier ircuits As we have developed different models for D signals (simple large-signal model) and A signals (small-signal model), analysis of JT circuits follows these steps: D biasing analysis:
More informationLab 7: Operational Amplifiers Part I
Lab 7: Operational Amplifiers Part I Objectives The objective of this lab is to study operational amplifier (op amp) and its applications. We will be simulating and building some basic op amp circuits,
More informationStudent Exploration: Circuits
Name: Date: Student Exploration: Circuits Vocabulary: ammeter, circuit, current, ohmmeter, Ohm s law, parallel circuit, resistance, resistor, series circuit, voltage Prior Knowledge Questions (Do these
More information6 Series Parallel Circuits
6 Series Parallel Circuits This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/. Air Washington
More informationSmall Signal Analysis of a PMOS transistor Consider the following PMOS transistor to be in saturation. Then, 1 2
Small Signal Analysis of a PMOS transistor Consider the following PMOS transistor to be in saturation. Then, 1 I SD = µ pcox( VSG Vtp)^2(1 + VSDλ) 2 From this equation it is evident that I SD is a function
More informationSeries and Parallel Resistive Circuits Physics Lab VIII
Series and Parallel Resistive Circuits Physics Lab VIII Objective In the set of experiments, the theoretical expressions used to calculate the total resistance in a combination of resistors will be tested
More informationBasic voltmeter use. Resources and methods for learning about these subjects (list a few here, in preparation for your research):
Basic voltmeter use This worksheet and all related files are licensed under the Creative Commons ttribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,
More informationMAS.836 HOW TO BIAS AN OP-AMP
MAS.836 HOW TO BIAS AN OP-AMP Op-Amp Circuits: Bias, in an electronic circuit, describes the steady state operating characteristics with no signal being applied. In an op-amp circuit, the operating characteristic
More informationCornerstone Electronics Technology and Robotics I Week 15 Combination Circuits (Series-Parallel Circuits)
Cornerstone Electronics Technology and Robotics I Week 15 Combination Circuits (Series-Parallel Circuits) Administration: o Prayer o Turn in quiz Electricity and Electronics, Chapter 8, Introduction: o
More informationTHE BREADBOARD; DC POWER SUPPLY; RESISTANCE OF METERS; NODE VOLTAGES AND EQUIVALENT RESISTANCE; THÉVENIN EQUIVALENT CIRCUIT
THE BREADBOARD; DC POWER SUPPLY; RESISTANCE OF METERS; NODE VOLTAGES AND EQUIVALENT RESISTANCE; THÉVENIN EQUIVALENT CIRCUIT YOUR NAME LAB MEETING TIME Reference: C.W. Alexander and M.N.O Sadiku, Fundamentals
More informationLecture 7 Circuit analysis via Laplace transform
S. Boyd EE12 Lecture 7 Circuit analysis via Laplace transform analysis of general LRC circuits impedance and admittance descriptions natural and forced response circuit analysis with impedances natural
More informationTutorial 12 Solutions
PHYS000 Tutorial 2 solutions Tutorial 2 Solutions. Two resistors, of 00 Ω and 200 Ω, are connected in series to a 6.0 V DC power supply. (a) Draw a circuit diagram. 6 V 00 Ω 200 Ω (b) What is the total
More informationOperational Amplifier - IC 741
Operational Amplifier - IC 741 Tabish December 2005 Aim: To study the working of an 741 operational amplifier by conducting the following experiments: (a) Input bias current measurement (b) Input offset
More informationAP1 Electricity. 1. A student wearing shoes stands on a tile floor. The students shoes do not fall into the tile floor due to
1. A student wearing shoes stands on a tile floor. The students shoes do not fall into the tile floor due to (A) a force of repulsion between the shoes and the floor due to macroscopic gravitational forces.
More informationhttp://users.ece.gatech.edu/~mleach/ece3050/notes/feedback/fbexamples.pdf
c Copyright 2009. W. Marshall Leach, Jr., Professor, Georgia Institute of Technology, School of Electrical and Computer Engineering. Feedback Amplifiers CollectionofSolvedProblems A collection of solved
More informationBJT Amplifier Circuits
JT Amplifier ircuits As we have developed different models for D signals (simple large-signal model) and A signals (small-signal model), analysis of JT circuits follows these steps: D biasing analysis:
More informationPower measurement in balanced 3 phase circuits and power factor improvement. 1 Power in Single Phase Circuits. Experiment no 1
Experiment no 1 Power measurement in balanced 3 phase circuits and power factor improvement 1 Power in Single Phase Circuits Let v = m cos(ωt) = cos(ωt) is the voltage applied to a R-L circuit and i =
More informationLecture 12: DC Analysis of BJT Circuits.
Whites, 320 Lecture 12 Page 1 of 9 Lecture 12: D Analysis of JT ircuits. n this lecture we will consider a number of JT circuits and perform the D circuit analysis. For those circuits with an active mode
More information12. Transformers, Impedance Matching and Maximum Power Transfer
1 1. Transformers, Impedance Matching and Maximum Power Transfer Introduction The transformer is a device that takes AC at one voltage and transforms it into another voltage either higher or lower than
More information3.1. Solving linear equations. Introduction. Prerequisites. Learning Outcomes. Learning Style
Solving linear equations 3.1 Introduction Many problems in engineering reduce to the solution of an equation or a set of equations. An equation is a type of mathematical expression which contains one or
More informationIntroduction to Paralleling of LTC Transformers by the Circulating Current Method
TAPCHANGER CONTROLS Application Note #11 Introduction to Paralleling of LTC Transformers by the Circulating Current Method 1.0 ABSTRACT This Application Note discusses the elements of paralleling load
More informationBipolar Transistor Amplifiers
Physics 3330 Experiment #7 Fall 2005 Bipolar Transistor Amplifiers Purpose The aim of this experiment is to construct a bipolar transistor amplifier with a voltage gain of minus 25. The amplifier must
More informationTransistor Amplifiers
Physics 3330 Experiment #7 Fall 1999 Transistor Amplifiers Purpose The aim of this experiment is to develop a bipolar transistor amplifier with a voltage gain of minus 25. The amplifier must accept input
More informationLab 2: Resistance, Current, and Voltage
2 Lab 2: Resistance, Current, and Voltage I. Before you come to la.. A. Read the following chapters from the text (Giancoli): 1. Chapter 25, sections 1, 2, 3, 5 2. Chapter 26, sections 1, 2, 3 B. Read
More informationDependent Sources: Introduction and analysis of circuits containing dependent sources.
Dependent Sources: Introduction and analysis of circuits containing dependent sources. So far we have explored timeindependent (resistive) elements that are also linear. We have seen that two terminal
More informationWHY DIFFERENTIAL? instruments connected to the circuit under test and results in V COMMON.
WHY DIFFERENTIAL? Voltage, The Difference Whether aware of it or not, a person using an oscilloscope to make any voltage measurement is actually making a differential voltage measurement. By definition,
More informationCollection of Solved Feedback Amplifier Problems
c Copyright 2009. W. Marshall Leach, Jr., Professor, Georgia Institute of Technology, School of Electrical and Computer Engineering. Collection of Solved Feedback Amplifier Problems This document contains
More informationSection 3. Sensor to ADC Design Example
Section 3 Sensor to ADC Design Example 3-1 This section describes the design of a sensor to ADC system. The sensor measures temperature, and the measurement is interfaced into an ADC selected by the systems
More informationTransistor Biasing. The basic function of transistor is to do amplification. Principles of Electronics
192 9 Principles of Electronics Transistor Biasing 91 Faithful Amplification 92 Transistor Biasing 93 Inherent Variations of Transistor Parameters 94 Stabilisation 95 Essentials of a Transistor Biasing
More information3: Nodal Analysis. E1.1 Analysis of Circuits (2015-7020) Nodal Analysis: 3 1 / 12. 3: Nodal Analysis
Current Floating Voltage Dependent E1.1 Analysis of Circuits (2015-7020) Nodal Analysis: 3 1 / 12 Aim of Nodal Analysis Current Floating Voltage Dependent The aim of nodal analysis is to determine the
More informationEnvironmental Monitoring with Sensors: Hands-on Exercise
Environmental Monitoring with Sensors: Hands-on Exercise Now that you ve seen a few types of sensors, along with some circuits that can be developed to condition their responses, let s spend a bit of time
More informationResistors in Series and Parallel
Resistors in Series and Parallel Bởi: OpenStaxCollege Most circuits have more than one component, called a resistor that limits the flow of charge in the circuit. A measure of this limit on charge flow
More information13.10: How Series and Parallel Circuits Differ pg. 571
13.10: How Series and Parallel Circuits Differ pg. 571 Key Concepts: 5. Connecting loads in series and parallel affects the current, potential difference, and total resistance. - Using your knowledge of
More informationDIGITAL-TO-ANALOGUE AND ANALOGUE-TO-DIGITAL CONVERSION
DIGITAL-TO-ANALOGUE AND ANALOGUE-TO-DIGITAL CONVERSION Introduction The outputs from sensors and communications receivers are analogue signals that have continuously varying amplitudes. In many systems
More informationChapter 19 Operational Amplifiers
Chapter 19 Operational Amplifiers The operational amplifier, or op-amp, is a basic building block of modern electronics. Op-amps date back to the early days of vacuum tubes, but they only became common
More informationTECH TIP # 37 SOLVING SERIES/PARALLEL CIRCUITS THREE LAWS --- SERIES CIRCUITS LAW # 1 --- THE SAME CURRENT FLOWS THROUGH ALL PARTS OF THE CIRCUIT
TECH TIP # 37 SOLVING SERIES/PARALLEL CIRCUITS Please study this Tech Tip along with assignment 4 in Basic Electricity. Parallel circuits differ from series circuits in that the current divides into a
More informationWHAT DESIGNERS SHOULD KNOW ABOUT DATA CONVERTER DRIFT
WHAT DESIGNERS SHOULD KNOW ABOUT DATA CONVERTER DRIFT Understanding the Components of Worst-Case Degradation Can Help in Avoiding Overspecification Exactly how inaccurate will a change in temperature make
More informationJ.L. Kirtley Jr. Electric network theory deals with two primitive quantities, which we will refer to as: 1. Potential (or voltage), and
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.061 Introduction to Power Systems Class Notes Chapter 1: eiew of Network Theory J.L. Kirtley Jr. 1 Introduction
More informationCommon-Emitter Amplifier
Common-Emitter Amplifier A. Before We Start As the title of this lab says, this lab is about designing a Common-Emitter Amplifier, and this in this stage of the lab course is premature, in my opinion,
More information